Question

What is the limit of (2−x)2(3−x)2(1−x)(2−x2)2 as x goes to infinity?

Answer 1

Divide by highest power of x:

2

+

1

x

2

4

x

2

−

1

lim

x

→

∞

2

+

1

x

2

4

x

2

−

1

=

2

+

0

0

−

1

=

−

2

Answer 2

Answer:

$\lim_{x \to \infty}( 2 - x )^2( 3 - x )^2( 1 - x )( 2 - x^2)^2\,=\infty$

Step-by-step explanation:

Let the function f (X) = ( 2 - x )²( 3 - x )²( 1 - x )( 2 - x² )²

To find the limit of function at infinity.

$\lim_{x \to \infty}f (X)\,=\,\lim_{x \to \infty} [( 2 - x )^2( 3 - x )^2( 1 - x )( 2 - x^2)^2]$

$=\lim_{x \to \infty}( 2 - x )^2( 3 - x )^2( 1 - x )( 2 - x^2 )^2}$

$=\lim_{x \to \infty}( 2 - x )^2\lim_{x \to \infty}( 3 - x )^2\lim_{x \to \infty}( 1 - x )\lim_{x \to \infty}( 2 - x^2 )^2}$

=∞